Related papers: Pairs of valuations and the geometry of soluble gr…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.

We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…

A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…

We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.

Consider pairs of the form (G, N), with G a group and N \normal G, as objects of a category \PG. A morphism (G_1, N_1) \To (G_2, N_2) will be a group homomorphism f : G_1 \To G_2 such that f(N_1) \subset N_2. We introduce a functor Q : \PG…

Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We give a criterion for a group homomorphism on a valued abelian group to be surjective and to preserve spherical completeness. We apply this to give a criterion for the existence of integration on a valued differential field. Further, we…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…

We show that the geometric and homological finiteness properties of group pairs are invariant under a suitable notion of quasi-isometry for group pairs.

Commensurable groups are bi-interpretable, under suitable definability conditions.

Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…

We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions